
To smooth trajectories, we can use a Kalman filter. The implemented KalmanSmootherCV is based on the assumption of a nearly-constant velocity (CV) model. To use KalmanSmootherCV, the optional dependency StoneSoup needs to be installed.
A closely related type of operation is trajectory generalization which is coverd in a separate notebook.
import pandas as pd
import geopandas as gpd
import movingpandas as mpd
import shapely as shp
import hvplot.pandas
import matplotlib.pyplot as plt
from geopandas import GeoDataFrame, read_file
from shapely.geometry import Point, LineString, Polygon
from datetime import datetime, timedelta
from holoviews import opts, dim
import warnings
warnings.filterwarnings('ignore')
plot_defaults = {'linewidth':5, 'capstyle':'round', 'figsize':(9,3), 'legend':True}
opts.defaults(opts.Overlay(active_tools=['wheel_zoom']))
hvplot_defaults = {'tiles':'CartoLight', 'frame_height':320, 'frame_width':320, 'cmap':'Viridis', 'colorbar':True}
mpd.show_versions()
MovingPandas 0.15.rc1 SYSTEM INFO ----------- python : 3.9.15 | packaged by conda-forge | (main, Nov 22 2022, 08:39:05) [MSC v.1929 64 bit (AMD64)] executable : H:\miniconda3\envs\mpd-ex\python.exe machine : Windows-10-10.0.19045-SP0 GEOS, GDAL, PROJ INFO --------------------- GEOS : None GEOS lib : None GDAL : 3.5.0 GDAL data dir: None PROJ : 9.0.0 PROJ data dir: H:\miniconda3\pkgs\proj-9.0.0-h1cfcee9_1\Library\share\proj PYTHON DEPENDENCIES ------------------- geopandas : 0.12.2 pandas : 1.5.3 fiona : 1.8.21 numpy : 1.24.1 shapely : 1.8.2 rtree : 1.0.0 pyproj : 3.3.1 matplotlib : 3.6.3 mapclassify: None geopy : 2.3.0 holoviews : 1.14.9 hvplot : 0.8.2 geoviews : 1.9.6 stonesoup : 0.1b11
gdf = read_file('../data/geolife_small.gpkg')
traj_collection = mpd.TrajectoryCollection(gdf, 'trajectory_id', t='t')
split = mpd.ObservationGapSplitter(traj_collection).split(gap=timedelta(minutes=15))
split.plot(column='trajectory_id', **plot_defaults)
<AxesSubplot: >
This smoother operates on the assumption of a nearly-constant velocity (CV) model. The process_noise_std and measurement_noise_std parameters can be used to tune the smoother:
process_noise_std governs the uncertainty associated with the adherence of the new (smooth) trajectories to the CV model assumption; higher values relax the assumption, therefore leading to less-smooth trajectories, and vice-versa.measurement_noise_std controls the assumed error in the original trajectories; higher values dictate that the original trajectories are expected to be noisier (and therefore, less reliable), thus leading to smoother trajectories, and vice-versa.Try tuning these parameters and observe the resulting trajectories:
smooth = mpd.KalmanSmootherCV(split).smooth(process_noise_std=0.1, measurement_noise_std=10)
print(smooth)
TrajectoryCollection with 11 trajectories
kwargs = {**hvplot_defaults, 'line_width':4}
(split.hvplot(title='Original Trajectories', **kwargs) +
smooth.hvplot(title='Smooth Trajectories', **kwargs))
kwargs = {**hvplot_defaults, 'c':'speed', 'line_width':7, 'clim':(0,20)}
(split.trajectories[2].hvplot(title='Original Trajectory', **kwargs) +
smooth.trajectories[2].hvplot(title='Smooth Trajectory', **kwargs))
traj = split.trajectories[2]
cleaned = traj.copy()
cleaned.add_speed(overwrite=True)
for i in range(0,10):
cleaned = mpd.OutlierCleaner(cleaned).clean({'speed': 1})
smoothed = mpd.KalmanSmootherCV(cleaned).smooth(process_noise_std=0.1, measurement_noise_std=10)
(traj.hvplot(title='Original Trajectory', **kwargs) +
cleaned.hvplot(title='Cleaned Trajectory', **kwargs) +
smoothed.hvplot(title='Cleaned & Smoothed Trajectory', **kwargs))